Later on Teukolsky [1]}, studied the same problem in Kerr geometry. While in the spherically symmetric case, the angular part completely decouples from the radial part, in the rotating case, the dynamics quite surprisingly separates but the separation constant, a.k.a. Carter constant [2]}, depends on the frequency of the perturbation and is not exactly known i. e. \(K^2= \ell (\ell +1) + {\cal O}(a_J\omega )\)  whereWe denote the ratio \(J/M\)  by \(a_J\) , since we will use \(a\)  and \(a_D\)  to denote the fundamental periods of the SW curve and \(a_f\)  to denote the radius of the circular profile later on. \(a_J=J/M\) .
